Solving systems of equations in supernilpotent algebras
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
Recently, M.\ Kompatscher proved that for each finite supernilpotent algebra $\ab{A}$ in a congruence modular variety, there is a polynomial time algorithm to solve polynomial equations over this algebra. Let $\mu$ be the maximal arity of the fundamental operations of $\ab{A}$, and let
\[ d := |A|^{\log_2 (\mu) + \log_2 (|A|) + 1}.\]
Applying a method that G.\ K{\'a}rolyi and C.\ Szab\'{o} had used to solve equations over finite nilpotent rings, we show that for $\ab{A}$, there is $c \in \N$ such that a solution of every system of $s$ equations in $n$ variables can be found by testing at most $c n^{sd}$ (instead of all $|A|^n$ possible) assignments to the variables. This also yields new information on some circuit satisfiability problems.